The shift of the color spectrum means that the peak intensity of the light is moving, as the temperature is raised, from infrared to red to yellow to blue. As the peak moves, the distribution of light among the wavelengths broadens. By the time the peak is at the blue, so many of the other colors are being radiated that the hot body appears to our eyes as white. White hot, we say. Today astrophysicists are studying the black body radiation left over from the most incandescent radiation in the history of the universe—the Big Bang.
But I digress. In the late 1890s, the data on black body radiation were getting better and better. What did Maxwell's theory say about these data? Catastrophe! It was just wrong. Classical theory predicted the wrong shape for the curve of distribution of light intensity among the various colors, the various wavelengths. In particular, it predicted that the peak quantity of light would always be emitted at the shortest wavelengths, toward the violet end of the spectrum and even into the invisible ultraviolet. This is not what happens. Hence "the ultraviolet catastrophe," and hence the smoking gun.
Initially, it was believed that this failure of the application of Maxwell's equations would be solved by a better understanding of how electromagnetic energy was generated by the radiating matter. The first physicist to appreciate the significance of this failure was Albert Einstein in 1905, but the stage was set for the master by another theorist.
Enter Max Planck, a Berlin theorist in his forties, who had had a long career in physics and was an expert on the theory of heat. He was smart, and he was professorial. Once, when he forgot which room he was supposed to lecture in, he stopped by the department office and asked, "Please tell me in which room does Professor Planck lecture today?" He was told sternly, "Don't go there, young fellow. You are much too young to understand the lectures of our learned Professor Planck."
In any case, Planck was close to the experimental data, much of which had been acquired by colleagues in his Berlin laboratory, and he was determined to understand them. He made an inspired guess at a mathematical expression that would fit the data. Not only did it fit the distribution of light intensity at any given temperature, but it agreed with the way the curve (the distribution of wavelengths) changed as the temperature changed. For future events it is important to emphasize that a given curve allows one to calculate the temperature of the body emitting the radiation. Planck had reason to be proud of himself. "Today I made a discovery as important as that of Newton," he boasted to his son.
Planck's next problem was to tie his lucky educated guess to some law of nature. Black bodies, so the data insisted, emitted very little radiation at short wavelengths. What "law of nature" could result in a suppression of the short wavelengths so beloved by classical Maxwell theory? A few months after publishing his successful equation, Planck hit on a possibility. Heat is a form of energy, and thus the energy content of the radiating body is limited by its temperature. The hotter the object, the more energy available. In classical theory this energy is distributed equally among the different wavelengths, BUT (get goose pimples, damn it, we are about to discover quantum theory) suppose the amount of energy depends on the wavelength. Suppose short wavelengths "cost" more energy. Then, as we try to radiate shorter wavelengths, we run out of available energy.
Planck found that to justify his formula (now called the Planck law of radiation) he had to make two explicit assumptions. He said, first, that the energy radiated is related to the wavelength of the light, and second, that discreteness is inextricably linked to this phenomenon. Planck could justify his formula and keep peace with the laws of heat by assuming that the radiation was emitted in discrete bundles or "packets" of energy or (here it comes) "quanta." Each bundle's energy is related to the frequency via a simple connection: E = hf. A quantum of energy £ is equal to the frequency, f, of the light times a constant, h. Since frequency is inversely related to wavelength, the short wavelengths (or high frequencies) cost more energy. At any given temperature, only so much energy is available, so high frequencies are suppressed. This discreteness was essential to get the right answer. Frequency is the speed of light divided by the wavelength.
The constant that Planck introduced, h, was determined by the data. But what is h? Planck called it the "quantum of action," but history calls it Planck's constant, and it will forevermore symbolize the revolutionary new physics. Planck's constant has a value, 4.11 × 10−15 eV-second, for what it's worth. Don't memorize. Just note that it's a very small number, thanks to the 10−15 (15 places past the decimal point).
This—the introduction of the notion of a quantum or bundle of light energy—is the turning point, although neither Planck nor his colleagues understood the depth of this discovery. The exception was Einstein, who did recognize the true significance of Planck's quanta, but for the rest of the scientific community it took twenty-five years to sink in. Planck's theory disturbed him; he didn't want to see classical physics destroyed. "We have to live with quantum theory," he finally conceded. "And believe me, it will expand. It will not be only in optics. It will go in all fields." How right he was!
As a final comment, in 1990 the Cosmic Background Explorer (COBE) satellite transmitted back to its delighted astrophysicist masters data on the spectral distribution of the cosmic background radiation that pervades all of space. The data, of unprecedented precision, fit the Planck formula for black body radiation exactly. Remember, the curve of distribution of light intensity allows one to define the temperature of the body emitting the radiation. Using the data from the COBE satellite and Planck's equation, the researchers were able to calculate the average temperature of the universe. It's cold here: 2.73 degrees above absolute zero.
SMOKING GUN NO. 2: THE PHOTOELECTRIC EFFECT
Now we zip over to Albert Einstein, working as a clerk in the Swiss Patent Office in Bern. The year is 1905. Einstein obtained his Ph.D. in 1903 and spent the next year brooding about the system and the meaning of life. But 1905 was a good year for him. He managed to solve three of the outstanding problems of physics that year: the photoelectric effect (our topic), the theory of Brownian motion (look it up!), and, oh yes, the special theory of relativity. Einstein understood that Planck's guess meant that light, electromagnetic energy, was being emitted in discrete globs of energy, hf, rather than in the classical idyll of emission, one wavelength continuously and smoothly changing to another.
This perception must have given Einstein the idea of explaining an experimental observation of Heinrich Hertz, who was generating radio waves to verify Maxwell's theory. Hertz did this by striking sparks between two metal balls. In the course of this work he noticed that sparks would jump across the gap more readily if the balls were freshly polished. He suspected that the polishing enabled the electric charge to leave the surface. Being curious, he spent some time studying the effect of light on metal surfaces. He noticed that the blue-violet light of the spark was essential in drawing charges out of the metal surface. These charges fueled the cycle by aiding the formation of sparks. Hertz reasoned that polishing removes oxides, which interfere with the interaction of light with a metal surface.
The blue-violet light was stimulating electrons to pour out of the metal, which at the time seemed a bizarre effect. Experimenters systematically studied the phenomenon and came up with these curious facts:
Red light is incapable of releasing electrons, even if the light is extraordinarily intense.
Violet light, even if relatively faint, releases electrons easily.
The shorter the wavelength (the more violet the light), the higher the energy of the released electrons.
Einstein realized that Planck's idea that light appears in bundles could be the key to understanding the photoelectric mystery. Imagine an electron, minding its own business in the metal of one of Hertz's highly polished balls. What kind of light can give that electron enough energy to jump out of the surface? Einstein, using Planck's equation, noted that if the wavelength of light is short enough, the electron receives enough energy to br
each the surface of the metal and escape. Either the electron swallows the entire bundle of energy or it doesn't, reasoned Einstein. Now, if the wavelength of the bundle swallowed is too long (not energetic enough), the electron cannot escape; it doesn't have enough energy. Drenching the metal with impotent (long-wavelength) bundles of light energy doesn't do any good. Einstein said that what's important is the energy of the bundle, not how many bundles you have.
Einstein's idea works perfectly. In the photoelectric effect the light quanta, or photons, are absorbed rather than, as with the Planck theory, emitted. Both processes seem to demand quanta with energy E = hf. The quantum concept was gaining. The photon idea wasn't convincingly proven until 1923, when American physicist Arthur Compton succeeded in demonstrating that a photon could collide with an electron much as two billiard balls collide, changing direction, energy, and momentum and acting in every way like a particle—but a very special particle somehow connected with a vibration frequency or wavelength.
Here was a ghost arisen. The nature of light was an old battleground. Recall that Newton and Galileo held that light consisted of "corpuscles." The Dutch astronomer Christiaan Huygens argued for a wave theory. This historic battle of Newton's corpuscles and Huygen's waves had been settled in favor of waves by Thomas Young's double-slit experiment (which we will review soon) early in the nineteenth century. In quantum theory, the corpuscle was resurrected, in the form of the photon, and the wave-corpuscle dilemma was revived with a surprise ending.
But there was even more trouble ahead for classical physics, thanks to Ernest Rutherford and his discovery of the nucleus.
SMOKING GUN NO. 3: WHO LIKES PLUM PUDDING?
Ernest Rutherford is one of those characters almost too good to be true, as if he were delivered to the scientific community by Central Casting. A big, gruff New Zealander with a walrus moustache, Rutherford was the first foreign research student admitted to the famed Cavendish Laboratory, run at the time by J. J. Thomson. Rutherford arrived just in time to witness the discovery of the electron. Good with his hands (unlike his boss, J.J.), he was an experimenter's experimenter a worthy rival to Faraday as the best ever He was known for his profound belief that swearing at an experiment made it work better a notion backed up by experimental results, if not theory. In evaluating Rutherford one must especially add in his students and postdocs, who, under his baleful eye, carried out great experiments. There were many: Charles D. Ellis (discoverer of beta decay), James Chadwick (discoverer of the neutron), and Hans Geiger (of counter fame), among others. Don't think it's easy to supervise some fifty graduate students. For one thing, one must read their papers. Listen to one of my best students begin his thesis: "This field of physics is so virginal that no human eyeball has ever set foot in it." But back to Ernest.
Rutherford had ill-concealed contempt for theorists, though, as you'll see, he wasn't such a bad one himself. And it's a good thing there wasn't the press coverage of science at the turn of the century that there is today. Rutherford was so quotable he'd have skewered himself out of a truckful of grants. Here are a few Rutherfordisms that have leaked down to us over the decades.
"Don't let me catch anyone talking about the universe in my department."
"Oh that stuff [relativity]. We never bother with that in our work."
"All science is either physics or stamp collecting."
"I've just been reading some of my early papers and, you know, when I finished, I said to myself, 'Rutherford, my boy, you used to be a damned clever fellow.'"
This damned clever fellow put in his time with Thomson, then crossed the Atlantic to work at McGill University in Montreal, then trekked back to England for a post at Manchester University. By 1908 he had won a Nobel Prize for his work with radioactivity. That would seem a fitting climax to a career for most men, but not for Rutherford. Now his work began in Ernest.
One cannot talk about Rutherford without talking about the Cavendish Lab, created in 1874 as the research laboratory of Cambridge University. The first director was Maxwell (a theorist as lab director?). The second was Lord Rayleigh, followed by Thomson in 1884. Rutherford arrived from the boonies of New Zealand as a special research student in 1895 at a fantastic time for rapid developments. One of the major ingredients for professional success in science is luck. Without this, forget it. Rutherford had it. His work on the newly discovered radioactivity—Becquerel rays they were called—honed him for his most important discovery, the atomic nucleus, in 1911. He made that discovery at the University of Manchester then returned in triumph to the Cavendish, where he succeeded Thomson as director.
You'll recall that Thomson had seriously complicated the issue of matter by discovering the electron. The chemical atom, thought to be the indivisible particle put forth by Democritus, now had little guys running around inside. These electrons had a negative charge, which presented a problem. Matter is neutral, neither positive nor negative. So what offsets the electrons?
The dramatic story begins quite prosaically. The boss comes into the lab. There sit a postdoc, Hans Geiger, and an undergraduate hanger-on, Ernest Marsden. They are engaged in alpha-particle scattering experiments. A radioactive source—for example, radon 222—naturally and spontaneously emits alpha particles. The alpha particles, it turns out, are nothing but helium atoms without their electrons—that is, helium nuclei, as Rutherford discovered in 1908. The radon source is placed in a lead case with a narrow hole that aims the alpha particles at a piece of extremely thin gold foil. As the alphas pass through the foil, their paths are deflected by the gold atoms. The angles of these deflections are the subject of the study. Rutherford had set up what became the historical prototype of a scattering experiment. You shoot particles at a target and see where they bounce. In this case the alpha particles were little probes whose purpose was to find out how atoms are structured. The gold-foil target is surrounded on all sides—360 degrees—by zinc sulfide screens. When a zinc sulfide molecule is struck by an alpha particle, it emits a flash of light, which allows the researchers to measure the angle of deflection. The alpha particle zips into the gold foil, hits an atom, and is deflected into one of the zinc sulfide screens. Flash! Most of the alpha particles are deflected only slightly and strike the zinc sulfide screen directly behind the gold foil. It was a tough experiment to do. They had no particle counter—Geiger hadn't invented it yet—so Geiger and Marsden were forced to sit in a dark room for several hours to adapt their eyesight to see the flashes. Then they had to spot and catalogue the number and positions of the little sparks.
Rutherford—who didn't have to sit in dark rooms because he was the boss—said: "See if any of the alpha particles are reflected from the foil." In other words, see if any of the alphas hit the gold foil and bounce back toward the source. Marsden recalled, "To my surprise I was able to observe the effect....I told Rutherford when I met him later; on the steps leading to his room."
The data, later published by Geiger and Marsden, recorded that one in 8,000 alpha particles was reflected from the metal foil. Rutherford's now-famous reaction to this news: "It was quite the most incredible event that ever happened to me in my life. It was as if you fired a fifteen-inch artillery shell at a piece of tissue paper and it came back and hit you."
This was May 1909. Early in 1911 Rutherford, acting now as a theoretical physicist, cracked the problem. He greeted his students with a broad smile. "I know what the atom looks like and I understand the strong backward scattering." In May of that year, his article declaring the existence of the nuclear atom was published. This was the end of an era. The chemical atom was now seen, correctly, as complex, not simple, and as cuttable, not at all a-tomlike. It was the beginning of a new era, the era of nuclear physics, and it marked the demise of classical physics, at least inside the atom.
Rutherford took at least eighteen months to think through a problem that is now solved by physics majors in their junior year. Why was he so puzzled by the ricocheting alpha particles? It had to do with how scientists a
t the time viewed the atom. Here is the massive, positively charged alpha particle charging into a gold atom and bouncing backward. The 1909 consensus was that the alpha should have blasted right through, like an artillery shell through tissue paper, to use Rutherford's metaphor.
The tissuelike model of the atom went back to Newton, who said forces have to cancel out if one is to have mechanical stability. Thus the electrical forces of attraction and repulsion had to be balanced in a stable atom that you could trust. The theorists of that turn-of-the-century epoch went in for a frenzy of model making, trying to arrange the electrons to make a stable atom. Atoms were known to have lots of negatively charged electrons. Therefore they had to have an equal amount of positive charge distributed in some unknown way. Since the electrons are very light and the atom is heavy, either an atom must have thousands of electrons (to make the weight) or the weight must reside in the positive charge. Out of the many models proposed, by 1905 the leading model of the day had been postulated by none other than J. J. Thomson, Mr. Electron. It was called the plum-pudding model because it had the positive charge spread out in a sphere covering the entire atom, with the electrons embedded throughout like plums in a pudding. Such an arrangement appeared to be mechanically stable and even allowed the electrons to vibrate around equilibrium locations. But the nature of the positive charge was a complete mystery.
The God Particle Page 20